Manuel Pellegrini has turned Manchester City into a attacking force that has scored 115 goals this season. Photograph: Gallo Images/Getty Images

For an insight into Manchester City's enigmatic manager, Manuel Pellegrini, rewind four years and Madrid's Museo Nacional Centro de Arte Reina Sofía. Back in May 2010, the Chilean was in charge of Real Madrid, though his tenure was about to end abruptly. Pellegrini had just taken Real to a record 96 points in La Liga to finish second behind Pep Guardiola's great Barcelona side when Florentino Pérez, the Real president, called.

Pellegrini was in the office of Manuel Borja, the director of the Reina Sofia, the Spanish capital's national museum of 20th-century art, when he spoke to Pérez. On finishing the call Pellegrini turned to Borja and said: "I think they're going to fire me." Arturo Salah, Pellegrini's closest friend for more than 40 years, says it comes as no great shock to discover that the Real Madrid manager was to learn of his fate while studying Picasso's Guernica and works by Damien Hirst, Man Ray and Francis Bacon.

"He loves art and museums all over the world," says Salah. "He is a great reader and possesses great culture which was taught by his parents and a consequence of his uncountable trips."

Within days of Pérez's telephone conversation Pellegrini had left Madrid. By November he had taken over at Málaga, before going on to replace Roberto Mancini last summer at City. Yet his inscrutable style means that despite the glare fixed on the world's richest club, beyond Pellegrini's penchant for attacking football that has piled up 115 goals this season and given City a chance of claiming an unprecedented quadruple, he remains largely unknown.

How this genteel 60-year-old could end a personal trophy drought since entering European management a decade ago by winning the Premier League title, the Champions League, the Capital One Cup and FA Cup is a story that began in his homeland. Pellegrini was a defender who played for Santiago's Universidad de Chile in a 13-year career that ended in 1986 with 28 international caps and no major honours.

Salah, who, when Chile manager in 1990, appointed Pellegrini as the Under-20 coach, says: "We had parallel lives as players and also as university friends with an education in engineering. Manuel has a strong personality, he has clear goals, so his actions and decisions are oriented towards those goals without falling into [complications]. He respects people and therefore demands respect. Values are above any other consideration. He is reliable and his word is worth more than any paper."

Roque Santa Cruz, the former City striker who played under Pellegrini at Málaga last season, says: "One of the best things he has is his football knowledge and the way he manages relationships with the players and staff. He is a genuine guy, very polite to people."

Pellegrini steered Málaga to last year's Champions League quarter-finals. He also guided Villarreal to a semi-final and quarter-final of Europe's elite club competition when in charge of the club for five years before his departure in 2009 for Real.

Santa Cruz says: "Pellegrini came and the club started to play a different way from what it was used to. He obviously plays a very attractive football, he loves the possession of the football. It comes with a lot of practice. That way of playing gives you the chance to really compete in the Champions League."

City are Pellegrini's 11th club in a career that has taken in Chile, Ecuador, Argentina and Spain. His first job included an ignominious relegation in his debut campaign managing Universidad de Chile. The 25th anniversary of that demotion, Universidad's first and only and on goal difference, was on 15 January. Pellegrini maintains he still owes a "big debt" to the Santiago club – among whose nicknames are El Romántico Viajero, the Romantic Traveller – blaming himself for leaving in mid-season for a fortnight to attend a managers' seminar in England.

Universidad de Chile, Palestino – in three separate spells – O'Higgins, Universidad Católica (all Chilean), LDU Quito (Ecuador), San Lorenzo, River Plate (Argentina), Villarreal, Real, Málaga and City form the roll call of Pellegrini's clubs. Yet Manuel Luis Pellegrini Ripamonti's move into coaching – or the sport at all – was hardly inevitable due to resistance from his family and the polio he fought hard to recover from when aged 11.

Pellegrini's late parents – mother, Silvia, and father, Emilio – wanted him to study. The grandson of Julio Pellegrini, an Italian from Tuscany who emigrated to Chile in the first decade of last century, he is one of eight children and the only one who has made a career in the game. While one sibling, Pablo, is an architect, and another, Silvia, a journalist, only Pedro, a lawyer who manages Pellegrini's contracts, has any involvement with football.

Pellegrini's desire to guard his privacy was illustrated when the Observer contacted Pedro. Speaking in perfect English Pedro politely declined to comment, saying: "It would go against the promise I have made to my brother."

With Emilio having created a successful family business, Constructora y Arquitectura, which flourished between the 1950s and 1970s, Pellegrini was urged to gain an academic grounding rather than pursue football. He chose both, taking classes from 8.30-10am at Pontificia Universidad Catolica, then training with Universidad de Chile – the institutions' clubs have a rivalry akin to that of City and Manchester United – from 10.30-1pm, before returning to class.

Pellegrini had wanted to be a doctor after going to Saint George's and Sagrados Corazones de Manquehue (Sacred Hearts of Manquehue), two private schools in east Santiago attended by wealthy families. But having been an honour pupil, the teenage Pellegrini failed the PAA, the Chilean university entrance test to take medicine.

Instead he decided on engineering. "It took me eight years to get my degree, not six like it was supposed," he said. "In that time there was no consideration for students who played sports. I studied in 'Católica' and played in 'La U' [Universidad de Chile] and you know what that means. It was not easy for me to get together and study because I was playing on the weekends. My greatest rival was structural calculus. The classes were given when I was training and I did what I could."

Pellegrini made his debut in September 1973 for Universidad, the same month the socialist government of President Salvador Allende was overthrown by the coup d'état of General Pinochet's armed forces. Pinochet's military junta ended 41 years of democracy in the country but Pellegrini has admitted to being "a dissident to the government of Salvador Allende and participated in several protests. The country was very complicated and so was I."

Pellegrini the player was moderately talented. Salah, with whom Pellegrini owns a sports complex, El Refugio, says: "I played against Manuel in the final years of my career. But we were team-mates for more than seven years in Universidad de Chile, him as a defender, me as a forward. Manuel was very efficient, always part of the starting line-up, had a great aerial game, was intelligent and a tactical player. His technique was adequate, but not his greatest asset. His assets were intelligence, physical condition and leadership that he learned from his position in the pitch."

Pellegrini, who is married to Carmen Gloria Pucci and has three sons, Manuel Jose, Juan Ignacio and Nicolas, realised his playing days were over when he came up against a young Ivan Zamorano, saying: "It was against Cobreandino [the Andes club now called Trasandino]. Our keeper deflected a shot and I jumped to head the ball away. A 17-year-old kid jumped at least half a metre and headed to the net. That day I decided I couldn't keep playing."

On retiring in 1986 he was again encouraged to enter the family business. But after helping the rebuilding effort following the damage caused by the earthquake in Algarrobo on the Chilean coast the year before that killed 177 and left around a million homeless, Pellegrini was convinced by his mentor, Fernando Riera, the former national coach who took Chile to the semi-finals of the 1962 World Cup on home soil, to enter management. He would go on to win cups in Chile – with Universidad Catolica - and titles in Ecuador (Quito) and Argentina (San Lorenzo and River Plate), though in Europe Pellegrini has claimed only the 2004 Intertoto Cup with Villarreal.

With a bullish and revitalised City challenging forcefully on four fronts that omission is set to change. On Monday José Mourinho, who replaced him at Real and is reinstalled at Chelsea, must somehow find a way of halting his side at the Etihad, where City have won 17 of 18 games this season and racked up 68 goals in 23 league games.

The Portuguese may decide against any attempt to get under the skin of the unreadable Pellegrini. "He never shouted," Santa Cruz says of his former manager. "He is very emotional but he keeps in a lot of disappointments at results because he is always very proud of his players and how they are putting in a lot of effort to perform and win. People who knew him expected his City team to be this good."